## Keywords, Theorems and Postulates

**Midsegments in Triangles**

- Midsegment
- Midsegment Theorem

**Perpendicular Bisectors and Angle Bisectors in Triangles**

- Perpendicular Bisector Theorem
- Perpendicular Bisector Theorem Converse
- Inscribe
- Circumscribe
- Angle Bisector Theorem
- Angle Bisector Theorem Converse

**Medians and Altitudes in Triangles**

- Median
- Centroid
- Median Theorem
- Altitude

**Inequalities in Triangles**

- Theorem 5-9
- Converse of Theorem 5-9
- Triangle Inequality Theorem
- SAS Inequality Theorem
- SSS Inequality Theorem

**Extension: Indirect Proof**

## Review

If and are the midpoints of the sides they lie on, find:

- The perpendicular bisector of .
- The median of .
- The angle bisector of .
- A midsegment.
- An altitude.
- A triangle has sides with length and . Find the range of the third side.

Fill in the blanks.

- A midsegment connects the __________ of two sides of a triangle.
- The height of a triangle is also called the __________.
- The point of intersection for all the medians of a triangle is the __________.
- The longest side is opposite the __________ angle in a triangle.
- A point on the __________ bisector is __________ to the endpoints.
- A point on the __________ bisector is __________ to the sides.
- A circle is __________ when it touches all the sides of a triangle.
- An __________ proof is also called a proof by contradiction.
- For and , and , then __________.

## Texas Instruments Resources

*In the CK-12 Texas Instruments Geometry FlexBook, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9690.*

### Image Attributions

## Description

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## Tags:

altitudes
angle bisector
angle bisectors
(17 more)
CK.MAT.ENG.SE.1.Geometry-Basic.5
CK.MAT.ENG.SE.2.Geometry.5
concurrency
indirect proof
inscribe
medians
mid-segment
Midsegment Theorem
midsegments
perpendicular bisector
perpendicular bisectors
proof
Segments
sides of triangles
triangle inequalities
Triangle Inequality Theorem
triangles

## Subjects:

## Date Created:

Feb 22, 2012## Last Modified:

Dec 11, 2014
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